The HRT Conjecture

The Linear Independence of Time-Frequency Translates Conjecture,
also known as the HRT conjecture, states that any finite set of
time-frequency translates of a given $L^2$ function must be linearly
independent. This conjecture, which was first stated in print in 1996,
remains open today. We will discuss this conjecture, its relation to
the Zero Divisor Conjecture in abstract algebra, and the (frustratingly
few) partial results that are currently available.